The mating habits of three- spined stickleback (a fish) have been studied intens

Question

The mating habits of three- spined stickleback (a fish) have been studied intensively. One experiment examined whether fish are re likely to mate with a member of the opposite sex that was similar in body size, rather than with fish that were different in size (McKinnon et al. 2004). The mating preferences were measured in nine different populations, and the preference was measured by an index that is zero if the population shows no preference for mating by size, positive if the population contains fish that prefer to mate with fish of adifferent size, and negative if the fish mate preferentially with individuals of the same size. Notice that the independent data points here are indices for each fish population The nine indices are as follows: -32.0,-29.8,-40.6,-90.8,-29.2,-28.8,-78.4,-59.2,-74.3 Test the hypothesis that, on average, sticklebacks do not mate differently by size. What can you conclude from these data?

Explanation / Answer

Here, all the nine indices are negative which indicates that they mate preferentially with individuals of the same size.

Ho: Sticklebacks do not mate differently by size

H1: Sticklebacks do mate with fish of adifferent size

Here the critical value of chi-square at 8 degrees of freedom for alpha 0.05(Two tailed) is 17.5345.

Hence we fail to accept the null hypothesis.

S.No. Observed Frequency(Of) Expected Frequency(Ef) Of-Ef (Of-Ef)^2 (Of-Ef)^2/Ef 1 32 51.46 -19.46 378.69 7.3590 2 29.8 51.46 -21.66 469.16 9.1169 3 40.6 51.46 -10.86 117.94 2.2919 4 90.8 51.46 39.34 1547.64 30.0745 5 29.2 51.46 -22.26 495.51 9.6290 6 28.8 51.46 -22.66 513.48 9.9782 7 78.4 51.46 26.94 725.76 14.1035 8 59.2 51.46 7.74 59.91 1.1642 9 74.3 51.46 22.84 521.67 10.1373 Average= 51.46 Total= 93.8543

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